C. Atkinson et S. Appleby, VARIATIONAL-PRINCIPLES DEVELOPED FOR AND APPLIED TO POROUS-ELASTIC SOLIDS, International journal of engineering science, 32(6), 1994, pp. 955-977
A dual variational principle is formulated for a general porous-elasti
c material in Laplace transform space. The material may be anisotropic
and spatially inhomogeneous. As an application of the theory, we cons
ider two problems of a crack in an infinite strip of inhomogeneous roc
k. In the first we bound the Stress Intensity Factor in both the trans
form and real time domains. For the second, we place bounds on a funct
ion of the poroelastic Stress Intensity Factor and pore pressure gradi
ent coefficient, in transform space. The bounds are compared with an e
ffective medium solution in both cases. We discuss the significance of
the method with regard to bounding effective properties in non-static
problems. We obtain, in implicit form, bounds on effective permeabili
ty for a rigid porous solid in transform space. These suggest the effe
ctive property is history dependent. Asymptotic methods are used to ob
tain large and small time results.